An infinite set of numbers (eg. all Real numbers greater than or equal to 1) can be represented in three different ways:

Graphing the set on a number line

Writing the set in inequality notation, eg. x≥1

Writing the set in interval notation, eg. [1,+∞)

When graphing on a number line, watch when to use "open" vs. "closed" circles on the endpoints. Inequality notation is pretty straight forward. Interval notation is the most commonly used method so learn it well.

Objectives

By the end of this topic you should know and be prepared to be tested on:

2.4.1 Sketch a solution set on a number line

2.4.2 Know the difference, on a number line, between an open and closed circle

2.4.3 State a solution set in inequality notation and in the closely related set-builder notation

2.4.4 State a solution set in interval notation

2.4.5 Know the difference, in interval notation, between the regular parenthesis ( and the square bracket [

2.4.6 Know to write intervals in the order of the number line, i.e. with the smaller number on the left

When studying your textbook for this lesson here are a few things to watch.

Some texts (irritatingly) emphasize set-builder notation over inequality notation. Set-builder is really an expanded form of inequality notation (just extra symbols -- more than necessary IMO). Rather than writing a solution in inequality notation e.g. x ≤ 1, they may use set-builder notation { x | x ≥ 1 } which is read "the set of all x such that x is greater than or equal to 1". The | bar means "such that". Some online testing systems will have you give the answer in set-builder notation, but they may write part of the notation for you as in { x | _____ } and all you have to do is write the inequality notation in the blank.

The most common notation used especially in later courses is interval notation. Watch the class discussion boards for mini-lessons about this notation. There are several specifics to remember when writing interval notation.